Zhiping Zhou

activity

20182026

collaborators

9 papers

math.QA2026

Monomial bases and canonical bases for quantum affine algebras

Toshiaki Shoji, Zhiping Zhou

We construct a monomial basis of a quantum affine algebra of simply-laced type, associated to the PBW basis of Beck-Nakajima. We show that there exists a simple algorithm of comput…

math.QA2025

Algorithm for computing canonical bases and foldings of quantum groups

Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative half of a quantum group of finite type. Let $P$ be the transition matrix between the canonical basis and a PBW basis of $U_{q}^{-}$ . In…

math.QA2025

Elementary construction of canonical bases, foldings, and piecewise linear bijections

Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative half of a quantum group of finite type. We construct the canonical basis of $U_{q}^{-}$ by applying the folding theory of quantum groups…

math.QA2022

Foldings of KLR algebras

Ying Ma, Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative half of the quantum group associated to a Kac-Moody algebra $g$ , and $U_{q}^{-}$ the quantum group obtained by a f…

math.QA2022

Diagram automorphisms and canonical bases for quantum affine algebras, II

Ying Ma, Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative part of the quantum enveloping algebra, and $σ$ the algebra automorphism on $U_{q}^{-}$ induced from a diagram automorphism. Let $\under…

math.QA2021

Diagram automorphisms and canonical bases for quantized enveloping algebras

Ying Ma, Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative part of the quantized enveloping algebra associated to a Kac-Moody algebra $g$ of symmetric type, and $U_{q}^{-}$ …

math.GR2020

Relationships among quasivarieties induced by the min networks on inverse semigroups

Ying-Ying Feng, Li-Min Wang, Zhi-Yong Zhou

A congruence on an inverse semigroup $S$ is determined uniquely by its kernel and trace. Denoting by $ρ_{k}$ and $ρ_{t}$ the least congruence on $S$ having the same kernel and the same…

math.QA2019

Diagram automorphisms and canonical bases for quantum affine algebras

Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-}$ be the negative part of the quantum enveloping algebra associated to a simply laced Kac-Moody Lie algebra $g$ , and $U_{q}^{-}$ the…

math.QA2018

Diagram automorphisms and quantum groups

Toshiaki Shoji, Zhiping Zhou

Let $U_{q}^{-} = U_{q}^{-} (g)$ be the negative part of the quantum group associated to a finite dimensional simple Lie algebra $g$ , and $σ : g \to g$ …